The recently discovered superconductor ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ has attracted significant attention due to its remarkably high transition temperature ($T_c$) under high pressure. Shortly after this discovery, thin-film ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ was demonstrated to exhibit ambient-pressure superconductivity; however, the corresponding $T_c$ is only about half that of the pressurized bulk material. This striking difference raises questions about the underlying mechanisms governing superconductivity in these two structures. To address this issue, we develop a phenomenological symmetry-based method to investigate the superconducting gap structure in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. Using density-functional theory methods ($\mathrm{DFT}+U$), together with the experimentally determined $T_c$ and structural symmetry, we find that both pressurized bulk and thin-film ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ exhibit $s_{\pm }$-wave pairing symmetry and two-gap superconductivity, yet their dominant microscopic pairing configurations are distinct. In the pressurized bulk, superconductivity is dominated by the out-of-plane pairing of the Ni-$d_{z^2}$ orbitals, while in the thin film, the in-plane pairing of the Ni-$d_{x^2-y^2}$ orbitals prevails. Furthermore, the observed reduction in $T_c$ can be attributed to this transition of the dominant pairing type, driven by the decreased ratio of interlayer to intralayer hoppings in the thin film. Our result sheds lights on the microscopic pairing in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ and reveals the significance of the symmetry. This method can potentially be generalized to a broader range of unconventional superconductors.

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• Superconductivity
• Nickelates
• Unconventional superconductors
• BCS theory
• Bogoliubov-de Gennes equations
• DFT+U
• Symmetries in condensed matter
• Tight-binding model